How chaotic are strange nonchaotic attractors?

Abstract

We show that the classic examples of quasi-periodically forced maps with strange nonchaotic
attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties.
More precisely, we show that these systems exhibit sensitive dependence on initial conditions,
both on the whole phase space and restricted to the attractor. The results also remain valid
in more general classes of quasiperiodically forced systems. Further, we include an elementary
proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the
structure of the attractor in an example with two-dimensional bers also introduced by Grebogi
et al.